Tunable Fabry–Pérot filter based on one-dimensional photonic crystals with liquid crystal components

A theoretical study of a tunable Fabry–Pérot multilayer structure composed of alternating layers of silicon and liquid crystal is presented and analyzed. The structure possesses two resonant frequencies within the stop band with tunable wavelengths and transmission properties. Tuning is achieved by allowing different orientations of the liquid crystal optical axes within the cavity and within the mirrors, while keeping the optical axes parallel to the layers. Applying the transfer matrix method for thin layers of anisotropic materials we demonstrate that the resonant wavelengths depend on the difference between the liquid crystal optical axis orientations. Besides, we are able to obtain a complete characterization of the structure in the form of its Jones matrix. From this, we propose an optical two-channel equalizer for applications around 1.55 μm that allows tuning the two resonant wavelengths and their relative amplitude levels.